Data classification on the geoid surface with grey wolf optimization

Abstract. Geoid determination is the process of modelling that enables the estimation of the height of a point with a known position. With the advancement of GNSS technologies, geoid determination has become one of the central problems in Geodesy. One of the critical issues in this process is identifying outliers in the data set and classifying data as compatible or outlier. This is because outlier points can significantly deteriorate the accuracy of the model and must be removed from the dataset. Traditionally, the identification of outlier measures in data classification has been carried out through statistical tests within the framework of the Least Squares (LS) method. However, recent developments in artificial intelligence and metaheuristic algorithms have provided powerful alternatives for solving complex optimization problems. One such problem is data classification. Among these algorithms, the Grey Wolf Optimizer (GWO), inspired by the social hierarchy and hunting strategy of grey wolves, has attracted increasing attention. In this study, the applicability of the data classification in GWO algorithm for outlier detection in geoid determination was investigated. The application area is located within the Ondokuz Mayıs University campus in Samsun province, and the dataset consists of 3555 points collected by GNSS/leveling measurements in a relatively flat and structure-free region. A second-degree polynomial surface was fitted to the dataset, and outlier detection was carried out using both LS and GWO methods. The LS method identified 493 outlier points, whereas the GWO classified 472 outlier points. A comparative analysis revealed that 181 points (38.35%) were commonly detected by both approaches, with a higher concentration in the upper and lower parts of the study area. The results demonstrate that GWO is capable of detecting a larger set of anomalous measurements compared to the conventional LS method. This indicates that GWO, by exploring the solution space globally, can capture additional outliers that might remain undetected by traditional statistical approaches. Therefore, the findings suggest that GWO can be considered a robust and complementary tool to classical methods.